Re: Mathematics and the Structure of Reality

From: Osher Doctorow <osher.domain.name.hidden>
Date: Tue, 3 Dec 2002 16:28:58 -0800

>From Osher Doctorow osher.domain.name.hidden, Tues. Dec. 3, 2002 1601

Tim,

I quote first your comment early in your posting on my RET theory.

[TIM]
I don't think the world's nonacceptance of "RET" means it is on par
> with category theory, just because some here don't think much of it.
>

[OSHER]
Next, I quote your own apparent sensitivity to your belief that somebody
might be attacking you, from later in the same posting.

[TIM] On your second point, about "how are you at depth?", I hope this
wasn't
> a cheap shot. Assuming it wasn't, I dig in to the areas that interest
> me....

[OSHER] What in the world are you talking about - what does depth have to do
with a cheap shot [question mark - my question-mark key is out]. And what
kind of a pun is that some here not thinking much of RET thereby not putting
it on a park with category theory. This last sentence, if it is not a cheap
shot, is definitely worthy of all the scientific research that can be
brought to bear on the typist of the sentence. First of all, there has been
no discussion with me participating in which somebody previously told me
that they don't think much of RET theory. Second, in the same posting, you
claim in effect to not understand RET theory. Those two sentences
approximately are all you say in this posting on RET theory. Then you go on
to generalize to quote some here not thinking much of RET unquote, which
gives the impression that there may be more than you, and you have not even
stated that you do not think much of it since you claim to not understand
it - which, incidentally, is far easier to explain than category theory [and
all my explanations of it are easier - that is the advantage of knowing
fuzzy multivalued logics, which apparently you do not], and so you have the
distinction of understanding what is harder to explain and not understanding
what is easier to explain - a phenomenon definitely worthy of the fullest
research to which science can be put.

Still, your replies are worthy of commenting upon because they pioneer new
directions in errors but also give some interesting references as a
redeeming feature. Your picture of Socrates is perhaps the funniest of
all your pictures, and that is especially interesting because you are
already in the non-fuzzy-multivalued-logic camp, so now you move into the
non-philosopher camp - which, believe it or not, is also where Smolin,
Rovelli, MacLane also are. So you think that in essence Socrates was an
idiot, the citizens of Athens were heroes, and Plato was a hero, and Sir
Roger Penrose was a hero. If you had the slightest background in philosophy
beyond philosophy 1 and 2, you would know that Plato wrote the biography of
Socrates - that nothing is known of Socrates beyond what his STUDENT Plato
wrote, and that Plato literally worshipped Socrates, and that Plato
described in detail how the horrible citizens of Athens destroyed Socrates
and forced him to take poison. Then, toward the end of your posting, you
claim that this Athens was nothing like the Athens you studied - even though
you cite Plato as one of the great philosophers in effect. One would have
to believe that you were there before Plato, somehow interposed between
Plato and his teacher Socrates, studying all this wisdom [from where, if I
may ask] and going around polling Athenians [certainly not examining the
psychology or culture or history of Athens - a poll would more likely
reflect the beliefs of conformists whether in science or politics].

Your master step, however, was your discovery that G. 't Hooft obtained the
Nobel Prize not from the Holographic Principle but from his work on the
electroweak force, contrary to my claim that he obtained it for the
Holographic Principle among other things. Most Nobel Laureates in physics
obtain their prizes for the so-called sum total of their work, although
specific highlights are often mentioned and apparently may be the only ones
mentioned. I assumed that 't Hooft's Holographic Principle was included.
In any case, if you think as you claim that the Holographic model is still
very hypothetical, you are out of line of what is one of the core concepts
of string, brane, supersymmetry, TQFT, loop theory, and on and on at the
present time. Since you keep referring me to your references, glance
through the arXivs in physics and mathematics from the 1997s through 2002.
Or read one of my explanations on one of the sites that I have cited in
previous postings.

I will conclude this posting with a summary of what I think your orientation
is. You, and your apparently closest hero John Baez, are COMPUTER PEOPLE.
Computer people, in my 64 years of experience in life, have almost always
near 0 verbal ability and about 50 percent quantitative ability on a scale
of 0 to 100. They have NO philosophical ability, which computers also
don't have, and their use of logic is confined to reading proofs of theorems
that have already been invented by somebody else and making stupid machines
move faster. They tend to like algebra, although even there they tend to
skip their assumptions since they don't have many of them. This lack of
philosophical orientation interferes with their understand of themselves and
their relationships to others, so that verbal aggression is prevalent in
their writings when replying to more capable thinkers.

Osher Doctorow



----- Original Message -----
From: "Tim May" <tcmay.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Tuesday, December 03, 2002 3:30 PM
Subject: Mathematics and the Structure of Reality


>
> On Tuesday, December 3, 2002, at 02:15 PM, Osher Doctorow wrote:
> > The
> > theorems that Tim has cited are one counterexample class to this, but
> > where
> > are the great predictions, where is there anything like the Einstein
> > Field
> > Equation, the Schrodinger Equation, Newton's Laws, Fermat's numerous
> > results, Maxwell's Equations, the Gauss-Bonnet Theorem and its
> > associated
> > equation that ties together geometry and topology,
> > Non-Euclidean/Riemannian
> > Geometry, Euclidean Geometry, the Jacobsen radical, Gauss-Null and
> > related
>
> Well, sure, these examples are typical of the massive breakthroughs in
> our understanding of the universe, and of the core fields of
> mathematics, that came in the 19th and early 20th centuries, roughly
> from 1850 to 1950. (There was a similar phase a bit earlier, with
> Newton, Leibniz, Laplace, Lagrange, etc.)
>
> This is an example of how the rate of discovery is _slowing down_.
>
> (I'll wait a moment for the jeers to subside...)
>
> By slowing down I mean of course that we have basically mapped out the
> larger structure of physics, and also chemistry, geology, math, and so
> on. Biology is perhaps much less mapped out.
>
> It's not likely that any theory, whether algebraic topology or model
> theory or whatever is going to give us anything like QM or relativity,
> for the reason that we have them and we have no evidence that some
> large body of experimental evidence awaits explanation in the way that
> the early QM reearchers knew they were explaining aspects of reality
> all around them (hydrogen atom, electron diffraction, spectral lines in
> emissions, radioactive decay, new and obvious particles like alphas,
> neutrons, positrons, muons, etc., and so on. Likewise, Einstein and
> others knew full well the import of the Michelson-Morley experiment.
> And the bending of light around the sun was predicted and then observed
> less than 2 years later. Finally, both theories came together with the
> atom bomb.
>
> Theories today are much, much further removed from experiment and from
> everyday implications. I don't need to say more about this, I presume.
>
> > sets in geometric nonlinear functional analysis, Godel's theorems, or
> > even
> > Hoyle's Law or the Central Limit Theorems or the almost incredible
> > theorems
> > of Nonsmooth Analysis and Kalman filters/predictors and Dynamic
> > Programming
> > and the Calculus of Variations and Cantor's cardinals and ordinals and
> > Robinson's infinitesimals and Dirac's equations and Dirac's delta
> > functions
> > and Feynmann's path history integrals and diagrams and the whole new
> > generation of continuum force laws and on and on.
>
> Here you're getting more modern areas, areas which in fact are deeply
> connected with topos theory, for example. Besides logic, which remains
> an active field with active researchers, you ought to look into
> "synthetic differential geometry," explored by Anders Kock and others.
> SDE reifies the infinitesimals. I would strongly argue that the
> nonsmooth analysis and infinitesimal analysis you crave is _more_
> closely related to Grothendieck toposes than you seem to appreciate.
>
> Likewise, check out papers by Crane, Baez, and others on the
> connections between Feynman diagrams and category theory. (One of them
> is "Categorical Feynmanology. The arXive site has them all.
>
> Kalman filters are just an applied tool. Check out "support vector
> machines" to see that work continues on new and improved tools of this
> sort.
>
> Expecting category theory to be a theory of dynamic programming or
> linear algebra practical programming is not reasonable.
>
>
> >
> > Sure, category theory can go in to many fields and find a category and
> > then
> > take credit for the field being essentially a category, and I can go
> > into
> > many fields and find plus and minus and division and multiplication
> > analogs
> > and declare the field as an example of Rare Event Theory [RET] or
> > Fairly
> > Frequent Event Theory [FFT or FET] or Very Frequent Event Theory [VFT
> > or
>
> I confess that I have never understand your "Rare Event Theory."
> Science is well-equipped to deal with events measured with large
> negative exponents, even probabilities with 10^-50 or whatever.
>
> I don't think the world's nonacceptance of "RET" means it is on par
> with category theory, just because some here don't think much of it.
>
> >
> > But string and brane theory are suffering from precisely what category
> > theory is suffering from - a paucity of predictions of the Einstein and
> > Schrodinger kind mentioned in the second paragraph back, and a paucity
> > of
> > depth. Now, Tim, you certainly know very very much, but how are you at
> > depth [question-mark - my question mark and several other keys like
> > parentheses are out].
>
> On your first point, yes, many current theories are very far from
> having testable predictions. Including, of course, the Tegmark theory,
> the Schmidhuber theory, and all sorts of universe-as-CA theories.
> String and loop quantum gravity theories may be hundreds of years away
> from being tested...or a test could surprise us within the next 10
> years, much as the evidence for black holes has mounted dramatically,
> faster than many of us 30 years ago thought it would.
>
> The reasons for this fall into two main categories (no pun intended).
> One, the low-hanging fruit point. A lot of bright minds have churned
> over things, with perhaps 1000 times as much effort as we had when
> Einstein was theorizing in his patent office, or even when the
> community of quantum mechanics experts was still small enough that they
> could meet a few times a year (a la Solvay Conferences) or meet with
> David Hilbert, Emmy Noether, Emil Artin, and John von Neumann in their
> offices at Gottingen and Heidelberg.
>
> The second reason is the energy one. It took a few thousand dollars's
> worth of equipment in 1900-1920 to produce interesting new particles,
> to prove the existence of electrons, protons, etc. Then it took maybe
> 10-20 that to build Cockroft-Walton and Van de Graf accelerators to
> find more. Then another similar increment in cost and energy for the
> early cyclotrons to find the interesting particles of the 1930s. Then
> another such factor to build nuclear piles and larger cyclotrons. And
> thus the 1950s saw a huge expenditure to build the Bevatron, where the
> antiproton and other particles were discovered/confirmed/created. (By
> the way, Dirac's prediction of antiparticles was a very "category
> theory"-like process of looking at symmetries in a commutative diagram
> and essentially saying "to make this diagram commute, I need this leg
> of the diagram.") And then we had multibillion dollar Brookhaven AGS
> machines, SLAC, and on to machines like Fermilab and CERN which cost
> many tens of billions. The Superconducting Supercollider was ultimately
> dropped due to incredible cost and low bang for the buck (perhaps only
> one new particle, according to many predictions.)
>
> Yeah, it's conceivable that the SSC would have produced some new realm
> of physics, as the enhancements going into CERN may still do. But the
> odds are against it. (John Cramer, he of the transactional
> interpretation of quantum mechanics, has some nice science fiction
> about this sort of thing: "Twistor." But it's SF, not anything that is
> likely to come out of CERN.)
>
> _These_ are the reasons we are in a sense "filling in the details,"
> fleshing out the tree whose branches grew to nearly their present form
> by the 1970s.
>
> It's one reason, I think, a lot of us who got started in physics in the
> 60s and 70s moved into other fields. (There was nothing of interest to
> me in S-matrix theory and Regge calculus, the "hot" areas of
> theoretical physics in 1972.)
>
> On your second point, about "how are you at depth?", I hope this wasn't
> a cheap shot. Assuming it wasn't, I dig in to the areas that interest
> me. As I have said more than a few times here, I am just in the past 8
> months or so digging in deeply to areas of logic (especially modal),
> brushing up on my math (algebra, topology, algebraic topology,
> analysis, etc.), and using topos and category theory as my touchstones.
> When I have gone as far as I wish to, perhaps I will move on to other
> areas.
>
>
>
> >
> > I will give an example. Socrates would rank in my estimation as a
> > Creative
> > Geniuses of Maximum Depth. The world of Athens was very superficial,
> > facially and bodily and publicly oriented but with relatively little
> > depth,
> > and when push came to shove, rather than ask what words meant, it
> > preferred
> > to kill the person making the inquiries.
>
> The death of Socrates notwithstanding, this does not sound like the
> Athens I studied. Socrates was a strange bird, and there is much
> evidence that he did everything he could to ensure his own death
> sentence. Equally profound thinkers like Plato and Aristotle faced very
> little pressure.
>
> > What it was afraid of was going
> > deep, asking what the gods really were,
>
> This doesn't match my reading of history. Aristotle asked profound
> questions about the nature of reality, metaphysics, belief, etc.
>
> > You mentioned, Tim, that the Holographic Model is still very
> > hypothetical.
> > Are we to understand that G. 't Hooft obtained the Nobel Prize for a
> > very
> > hypothetical idea [question-mark] among others.
>
> Ah, but 't Hooft did not get the Nobel for his work with Susskind and
> others on the holographic model. He got it for his work on the
> electroweak force.
> >
> > I will conclude this rather long posting with an explanation of why I
> > think
> > Lawvere and MacLane and incidentally Smolin and Rovelli went in the
> > wrong
> > direction regarding depth. It was because they were ALGEBRAISTS -
> > their
> > specialty and life's work in mathematics was ALGEBRA - very, very
> > advanced
> > ALGEBRA. Now, algebra has a problem with depth because IT HAS TOO MANY
> > ABSTRACT POSSIBILITIES WITH NO [MORE CONCRETE OR NOT] SELECTION
> > CRITERIA
> > AMONG THEM. It is somewhat like the Ocean - if an explorer worships
> > the
> > Ocean, then he will go off in any direction that Ocean seems to be
> > leading
> ...
>
> Sorry, but this is a silly argument. Smolin and Rovelli may in fact be
> wrong in their theory of loop quantum gravity (and the closely related
> theories of spin foams, etc., along with Penrose, Susskind, Baez,
> Ashketar, and the whole gang), but it is almost certainly not for some
> simplistic reason that they were "ALGEBRAISTS."
>
> In fact, Penrose is a geometer's geometer. See, for example, the essays
> in his Festschrift. Now the geometry focus of Penrose does not prove
> _anything_ about either the internal consistency or the ultimate truth
> of some of his spin network and spinor models, nor about the truth or
> falsity of spin foams and so on.
>
> As for Lawvere and Mac Lane being "ALGEBRAISTS," I neither see your
> point nor its relevance. What Mac Lane may or may not be is open to
> debate...his work on homology theory tends to mark him as an algebraic
> topologist. And Grothendieck and Lawvere were looking into
> generalizations of the concept of a space--and they succeeded.
> (Personally, and speculatively, when the concept of a space is
> generalized so nicely, I think in terms of "this probably shows up in
> the physical world or its description someplace." If this ain't
> geometry affecting a physics outlook, what is?)
>
> Anyway, it's silly to argue along these lines. You ought to take a look
> at one of his recent books (co-authored when he was around 80):
> "Sheaves in Geometry and Logic: A First Introduction to Topos Theory."
> I'd call sheaves, presheaves, and locales some pretty deep
> geometrical/topological ideas, albeit at a level of abstraction that
> takes a lot of effort to master.
>
> What the structure of reality really is depends on a couple of
> important things:
>
> 1. What aspect we are looking at, whether the local causal structure of
> spacetime or the "explanation" of the particles and their masses, or
> even at some grossly different scale, such as fluid turbulence (still
> not understand, in many ways, and yet almost certainly not depending on
> theories of branes or strings or the Planck-scale structure of
> spacetime).
>
> 2. Scales and energies, whether the cosmological or the ultrasmall.
>
> 3. Our conceptual biases (if we only know geometry, we see things
> geometrically, and so on).
>
> One of the reasons I like studying math is to expand my conceptual
> toolbox, to increase the number of conceptual basis vectors I can use
> to build models with.
>
>
> --Tim May
>
Received on Tue Dec 03 2002 - 19:44:33 PST